Former President Donald J. Trump drew criticism from several fellow Republicans on Sunday for his demeaning insults of Vice President Kamala Harris, a day after he called her “mentally disabled” and “mentally impaired” at a rally.

Senator Lindsey Graham, a South Carolina Republican, pushed back on Mr. Trump’s remarks on Sunday. “I just think the better course to take is to prosecute the case that her policies are destroying the country,” Mr. Graham said on CNN, adding that he did not think Ms. Harris was crazy but did think her policies were.

Representative Tom Emmer — a Minnesota Republican who has been helping Senator JD Vance of Ohio, Mr. Trump’s running mate, prepare for his upcoming debate — also sought to distance himself from Mr. Trump’s personal attacks. “I think we should stick to the issues,” Mr. Emmer said on ABC News.

Larry Hogan, a former Republican governor of Maryland who is currently running for the Senate, offered a sharper rebuke.

“I think that’s insulting not only to the vice president, but to people that actually do have mental disabilities,” Mr. Hogan, who has often criticized Mr. Trump in the past, said on CBS News. “I’ve said for years that Trump’s divisive rhetoric is something we can do without.”

Steven Cheung, the communications director for the Trump campaign, did not directly address Mr. Trump’s insults or the critical responses they had prompted. He instead argued that Ms. Harris’s record on immigration and border security made her “wholly unfit to serve as president.”

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